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At a Glance
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
Six Discs
Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?
Equilateral Areas
ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF.
Age 14 to 16 Challenge Level:
The area of a square inscribed in a circle with a unit radius is, satisfyingly, $2$.
What is the area of a regular hexagon inscribed in a circle with a unit radius?
What is the area of an equilateral triangle inscribed in a circle with a unit radius?
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.